Curious. Games are fun specifically because they are NOT real world. Instead games are abstractions, yet are “fun”.

This is all.

– Creator of shikakuroom.com

Paul.

I was supposed to spend some time building a forecasting model for UK interest rates based on various economic indicators. Instead, I spent time formulating a model of the break-even cost for aged port (a problem hinted at by your post /?p=18174). To be clear, this has no relevance for my professional work. Also, actually, I didn’t spend much time on the wine model, but I found it really difficult to stay away from it!

In contrast, another co-worker was meant to be recoding some of his old models and, instead, felt compelled to work on my interest rate/economics model!

I feel this is also somehow the punchline behind some of the Vi Hart videos: the math is really fun when done subversively.

I don’t know how to engineer this as a classroom technique.

Collatz Conjecture is one of my favorite “Fake-math” topics to explore with students. I wrote about how I explored it last year with my 5th/6th grade class.

http://artofmathstudio.wordpress.com/2013/10/06/fun-with-collatz-conjecture/

Perhaps what make it most intriguing is that it is simple to state, yet has eluded some of the most brilliant mathematicians’ attempts at proof. I usually drop in the discussion that a proof of this conjecture could even earn you an honorary Ph. D, or at the very least instant rock-star status in the math world.

Also students can have minor victories along the way to keep them motivated to explore, like proving that all powers of 2 will eventually go to 1.

Paper Pool: I like the version from Illuminations, though it was in CMP before that, and the problem is at least a century old:
http://illuminations.nctm.org/Activity.aspx?id=4219

Product Value Problem: I first heard this from John Horton Conway on NPR:
Find an English word for which the product of its letters (i.e., the product of the letters’ positions in the alphabet) is 3,000,000.
http://mathjokes4mathyfolks.com/problem_productvalue.html

Name Letters: A completely ridiculous 29-equation system that doesn’t LOOK like a system of equations problem, and kids just dig it:
http://mathjokes4mathyfolks.com/problem_namevalue.html
(For this one, I think the appeal is that the question asks students to find the value their name, which makes it personal.)

I agree. The use of the word “immediate” is misleading as I think it’s more of a spectrum. With Sudoku I think the feedback is still immediate enough to create engagement on easy puzzles and the feedback becomes less immediate on harder
puzzles.

In fact I’d say that you can control the challenge of any given puzzle or challenge by varying the immediacy of the feedback loop. Creating a feedback loop that is instantaneous may actually make a challenge too easy, potentially reducing engagement.

That said I think most of the time your better off providing more immediate feedback if you are looking for engagement. You can tackle more challenging problems more easily with a fast and consistent feedback loop, so the threat of making a challenge too easy can be compensated for through a more challenging problem.

Jared Cosulich:

When you look at what is going on in a puzzle (everything from a jigsaw puzzle to Tetris to Angry Birds) you see some very consistent patterns:

1) A clear goal that is neither too easy or too hard.

2) Immediate feedback loops enabling someone to develop and quickly test hypotheses.

The first is pretty well-supported. I find the second one problematic, though. When you play Sudoku, you write a number in a square and there’s no immediate feedback that it was the right or wrong number for that square. The feedback comes much later when you’ve realized you’ve created a logical contradiction.

wwntd:

But I think something that a lot of the posted math-tasks have in common is that students know when they’re done. They can solve a puzzle (a la, Ben Orlin’s distinction between game and puzzle) and know that the answer is done.

So there is eventual feedback, not simply immediate feedback. And that feedback has a certain character. Something to do with validation. The Sudoku book has answers in the back, but you can validate it yourself by verifying that your solution meets every constraint.

Mike Lawler:

Why is it fun? Even now, more than 25 years after seeing this result for the first time, it still surprises me. If you watch the video, you’ll see that the kids were floored. The fact that you get more or less the same picture from any starting point is also incredibly surprising.

“Surprise” is surfacing a lot around here.

Jason Dyer:

Part of what turns a “classroom math problem” into a “puzzle” is simple presentation. A Professor Layton game for the DS can get away with a system of linear inequalities if it is presented as different colors of cats.

I can’t tell if this is a joke or not.

Chris Hunter:

Sometimes, I think teachers mistakenly believe it is the context, rather than the math, that engages students. Area vs. Perimeter problems, brought up above, are examples of this. I can present the problem as “You have 24/240 m of fencing. Build the largest pen for your pet dog/dragon.” Real? Fantasy? Dunno. Doesn’t matter. Spot/Sparky are quickly forgotten. What engages students is the challenge of finding the largest area given the perimeter constraints.

A couple of points worth highlighting here:

1.) Optimization problems have a certain appeal, not necessarily for their competitive angle, but because they give everyone a place to start and then improve.

2.) When I find a productive and fun real-world task, it’s almost always the case that the “real world-ness” is its least salient aspect.

Michael Pershan:

When you started this series, I thought that you were attacking a scapegoat. Who really thinks that the only math that’s interesting to kids is “real world” math?

Kind of a few. This is a recurring topic of conversation between Mr. Mathalicious and me also.

Michael Pershan:

This is a different sort of “real world” than your snowboarder. But is it related? Does the idea that kids are into the real world spring from this notion that kids are interested in job prep?

The job world is a subset of the “real world” but the idea that kids will dig into math if teachers enforce its connections to the job world is problematic.